Chemical composition of multi-elemental thin films grown on a substrate critically affects the films' electrical, optical, as well as mechanical and other properties which are important for the films' practical applications. The chemical composition may be defined as a set of relative values, i.e., atomic concentrations of chemical elements present in a film of interest with respect to a concentration of one of the chemical elements in the film.
A spectroscopic approach has been developed in the industry to obtain a chemical composition by analyzing relative intensities of characteristic X-ray lines corresponding to the elements present in a material under study. Some examples of related spectroscopic techniques include the Energy Dispersive X-ray Spectrometry (EDS) and the X-ray Fluorescence (XRF). The EDS technique is based on the analysis of X-rays emitted from a surface exposed to an impact of an energetic electron beam. The XRF technique utilizes an X-ray source to excite the characteristic radiation.
Shortcomings of the existing X-rays spectrometry techniques for the quantitative composition analysis include the inability to obtain a direct proportionality between the measured intensity of an elemental X-ray line and the concentration of a corresponding chemical element.
Specifically, for the EDS technique, the reasons for such shortcomings are the complex interactions between the electron beam and the material under study, as well as between the X-ray and the material under study. The core of such complexity is the parametric nature of the problem, i.e., unknown parameters to be determined are part of the very equations and factors describing those interactions. This is aggravated by multiple compositionally dependent inter-element effects (for example, dependence of the intensity of one element line on the concentration of another element) as presented in “Scanning electron microscopy and X-ray microanalysis”, J. Goldstein, et al., Ch. 9-10, 3rd edition, Springer, 2003; and Massachusetts Institute of Technology, Electron Microprobe Facility, “Electron Microprobe Analysis”, Course 12.141, Lecture Notes by Dr. N. Chatterjee.
A number of models have been developed for calculation of an X-ray profile generated by decelerating electrons. However, these models are not satisfactory due to the fact that the spatial distribution of X-rays generation density inside films lacks uniformity and depends on elemental concentrations itself, as well as due to their inability for precise determination of atomic factors needed for the calculations.
Another difficulty of the chemical composition determination, is that, once generated in the volume of the material under study, X-rays experience absorption along their path to the film surface. A degree of such absorption, and thus the intensity of X-rays registered by an outside sensor, is, similar to the spatial distribution, parametric due to its dependency on the material composition.
A technique has been developed in the industry for the chemical composition determination based on utilization of standardized material samples (“Quantitative X-ray fluorescence analysis of samples of less than infinite thickness: difficulties and possibilities”, Rafal Sitko, et al., Spectrochimica Acta, Part B, Atomic Spectroscopy 64(11-12), pp. 1161-1172, October 2009; and “Electron beam induced x-ray emission: An in situ probe for composition determination during molecular beam epitaxy growth” Joseph G. Pellegrino, et al., Appl. Phys. Lett. 73, 3580 (1998)). In this approach, in order to link the emitted X-ray lines intensities to elemental concentrations, multiple calibrations are performed on bulk material samples of a known composition. The calibrations are processed by specific software to obtain the composition. The computations in this material standard based approach are overly complicated when applied to analyzing multi-elements materials (films) which contain a wide variety of elements. In addition, some calibration techniques require extra measurements to be performed with varying energies or with varying angles of an incident electron beam.
Another theoretical approach for determining films' chemical compositions relies on computations of multiple “matrix corrections” (ZAF) factors, which are applied to measured X-ray line intensities (“The quantitative analysis of thin specimens: a review of progress from the Cliff-Lorimer to the new ζ-factor methods”, M. Watanabe, D. B. Williams, Journal of Microscopy, vol. 221, Pt.2, February 2006, pp. 89-109; Oxford Instruments, “EDS for TEM explained”; and JEOL, XM-17330/27330, “Basic Software/Quantitative analysis program”). The computations take into account effects of chemical elements' atomic number, absorption, fluorescence, etc. Due to the complexity of interrelations between the material parameters and material interaction with the electron beam and X-rays, corrections are calculated based on numerous models which require an extensive database of X-ray parameters. Some values of elements and the material's factors needed for these computations often are not known accurately, or not applicable directly to experimental conditions.
For thin films, the situation is more complex due to the fact that the intensity of the X-ray emitted by a film depends on its thickness.
The knowledge of a film's thickness is also necessary for the accurate composition quantification of the film, which requires another layer of additional measurements and/or theoretical modeling. Moreover, not only the geometrical thickness of the film under study, but also topological difference between the standard samples and the real material surface (roughness, micro-particles, etc.) can strongly affect the measurements result.
The shortcomings of the existing techniques may contribute to somewhat “insufficient” analytical performance of the EDS which is regarded as only a “semi-quantitative” technique, due to the fact that the chemical composition measured through the EDS approach for thin films' chemical composition determination generally severely deviate from a true chemical composition.
Another disadvantage of the typical electron probe microanalysis systems is the electron beam positioning at 90° relative to the film surface. This arrangement is deficient in that the generation of X-rays occurs mostly inside the substrate, but not in the thin films of interest. Typical penetration ranges of energetic electrons in solids is approximately several microns, which is larger than ≦100 nm thickness of the films of interest. If electrons are incident on the film at a large angle to the surface (for example, perpendicular to the surface), they travel inside the film a small fraction of their total penetration range, and the probability of X-rays generation for the film's elements is low.
Additionally, a small incidence angle of the electron beam is not desired due to scattering of a large number of the beam electrons from the surface for incidence angles below 3 degrees, resulting in that the scattered beam electrons are prevented from contributing to the X-rays generation.
Thus, a long-lasting need exists in the thin films manufacturing to address the aforementioned deficiencies of thin films composition analysis, and to obviate deficiencies of the existing systems and approaches by relying neither on the standard bulk samples calibrations, theoretical modeling, nor on prior knowledge of films' thicknesses.
In addition it is desirable to provide a technique for the X-ray analysis where the beam electrons contribute into the X-ray generation in the most efficient manner.